Bezáková, Ivona ;
Curticapean, Radu ;
Dell, Holger ;
Fomin, Fedor V.
Finding Detours is FixedParameter Tractable
Abstract
We consider the following natural "above guarantee" parameterization of the classical longest path problem: For given vertices s and t of a graph G, and an integer k, the longest detour problem asks for an (s,t)path in G that is at least k longer than a shortest (s,t)path. Using insights into structural graph theory, we prove that the longest detour problem is fixedparameter tractable (FPT) on undirected graphs and actually even admits a singleexponential algorithm, that is, one of running time exp(O(k)) * poly(n). This matches (up to the base of the exponential) the best algorithms for finding a path of length at least k.
Furthermore, we study a related problem, exact detour, that asks whether a graph G contains an (s,t)path that is exactly k longer than a shortest (s,t)path. For this problem, we obtain a randomized algorithm with running time about 2.746^k * poly(n), and a deterministic algorithm with running time about 6.745^k * poly(n), showing that this problem is FPT as well. Our algorithms for the exact detour problem apply to both undirected and directed graphs.
BibTeX  Entry
@InProceedings{bezkov_et_al:LIPIcs:2017:7479,
author = {Ivona Bez{\'a}kov{\'a} and Radu Curticapean and Holger Dell and Fedor V. Fomin},
title = {{Finding Detours is FixedParameter Tractable}},
booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
pages = {54:154:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770415},
ISSN = {18688969},
year = {2017},
volume = {80},
editor = {Ioannis Chatzigiannakis and Piotr Indyk and Fabian Kuhn and Anca Muscholl},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/7479},
URN = {urn:nbn:de:0030drops74790},
doi = {10.4230/LIPIcs.ICALP.2017.54},
annote = {Keywords: longest path, fixedparameter tractable algorithms, aboveguarantee parameterization, graph minors}
}
2017
Keywords: 

longest path, fixedparameter tractable algorithms, aboveguarantee parameterization, graph minors 
Seminar: 

44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Issue date: 

2017 
Date of publication: 

2017 